Ask Mr. Smarty Plants

The most likely explanation for having a white Turk's cap flower is a recessive genetic mutation that occurred in the chemical pathway that produces the normal red color of the flower.  Whoever found the first white one realized it was a mutation, suspected it was a recessive mutation and (in order to develop pure-breeding white flowers) isolated the plant so that it didn't get pollen from red-flowered plants.   Malvaviscus arboreus var. drummondii (Turk's cap or turkscap) is pollinated by insects (bees, moths, butterflies) and by hummingbirds. Since you have red Turk's caps away from but still in the general vicinity as your white ones, one of the pollinators obviously was successful in transferring the red flowers' pollen to one of your white plants that then made the seed to produce the red-flowered plant among your white ones.  You may have been lucky for several years to keep your white flowers all pure white because they may not be as attractive to pollinators as the red ones are.  To maintain your white flowers without having red flowers among them you should certainly remove those red-flowered ones so that they are not close enough to easily furnish pollen to pollinate the white ones.  The white and red flowers will cross and eventually you will have more red flowers than white.

Now, for the longer explanation, I'm going to remind you and other readers of some of the basics of genetics in general and plant genetics in particular. Every individual plant has in its DNA, two copies of each of the genes that determine how it looks and how it functions.  This includes the genes that are responsible for flower color.  In general, the pigments that produce the colors of flowers are formed in a biochemical pathway that requires converting one substance to another substance using enzyme catalysts at every step until the pigment is formed.  If an enzyme that catalyzes any of the steps in the biochemical pathway doesn't function properly, then the pigment is NOT formed.  Let's consider, for instance, the pigments called anthocyanins that produce purple flowers.  Let's suppose that there are two different forms (alleles) of one of the genes that makes an enzyme in the biochemical pathway to the anthocyanin pigment.  One form of that enzyme works perfectly, the pigment pathway is completed and you get purple pigment.  The other form of the gene is defective and the enzyme it makes won't complete the pathway and there is NO pigment made.  There are then several possibilities.  Let's call the form of the gene that will result in one of the anthocyanins and purple pigment being made, 'A', and the form that won't produce purple pigment, 'a'.  There are 3 combinations—its genotype—for the two forms for any particular plant.  The plant could be A/A (have two copies that make pigment) or A/a (have one copy that does make pigment and one that doesn't make pigment) or a/a (has two copies that do NOT make pigment).  It's pretty easy to see that flowers with the genotype A/A will have purple flowers and those with the genotype a/a will have white flowers (lacking any pigment).  The puzzle is: what is the color of the flowers made by the genotype A/a.  If the A form of the gene can make enough enzyme to complete the pathway for all the anthocyanin that needs to be produced, then the flowers will be purple and we have "complete dominance"—that is, it takes only one copy of A for the flowers of genotype of A/a to look just like the flowers of genotype A/A.  [This is the explanation for the flower color of Mendel's pea plants, although the symbols usually used in the explanation for Mendel's pea colors are 'P' and 'p', instead of 'A' and 'a'.]  However, if having only one copy of A doesn't make enough enzyme to always complete the pathway, then flowers with the genotype of A/a will have a color (lavender or pink) intermediate between purple and white. This is called "incomplete dominance" with the appearance (or phenotype) something between the two extremes.  One flower whose flower color genetics have been studied, Mirabilis jalapa (Four-O-Clock), a native of South America, shows "incomplete dominance" with an A/A genotype showing dark magenta flowers, an a/a showing white flowers and A/a having pale pink flowers. 

If we use 'R' to indicate the 'red' allele for your Turk's cap and 'r' to indicate the white allele, then the genotype of your white ones must be r/r and the great majority of the red ones that are in another location have the genotype of R/R. (Although it is possible that a small number of your red flowers received 'r' pollen from the white plants and are R/r plants.)  It's easy to see if your red ones are pollinated by the other red ones in their location, it will be R/R x R/R and the only outcome is R/R = red.  The same for the white ones: r/r x r/r is r/r = white.   When your white plants ova received red pollen, the result was R/R x r/r = R/r = red—complete dominance.  The tricky thing is when you cross the R/r plants.   R/r plants can make 'R' ova and 'r' ova and they can also make 'R' pollen and 'r' pollen so the result of crossing two R/r plants is:

'R' pollen x 'R' ova = R/R = red

'R' pollen x 'r' ova = R/r = red

'r' pollen x 'R' ova = r/R = red

'r' pollen x 'r' ova = r/r = white

You can see that 3/4 of the plants will have red flowers and only 1/4 will have white.   You can also see that you want to isolate the white ones from the red ones as much as possible because, if left among the white ones, the red ones will gradually become the predominate color.