What would be a reason for a tree to have flowers of different colors?
There are a couple of possibilities for what's going on here:


The most likely explanation is Position Effect Variegation (PEV). Genes are, at the most basic level, organized linearly on chromosomes (very long strings of DNA). Some parts of chromosomes contain stretches of genes that are actively silenced, or turned off, by cells (large silenced regions like this are called heterochromatin). The boundaries of where this silencing starts and ends are sometimes fuzzy. If a gene necessary to produce pigment happens to be next to a silenced region, the silencing can randomly creep in and shut off that gene as well, or creep back to its normal boundary. (This is why it's called 'position' effect variegation: it depends on the physical position of a gene, in this case the pigment gene, on the chromosome, and how close it happens to be to a normally 'silenced' region.) This process is (probably) effectively random, so it won't happen in every cell, which means some cells will produce pigment whereas others won't. A famous example of this happens in fly eyes, as in the image on the left. Importantly, the difference here isn't 'genetic' (the actual content of the DNA), but 'epigenetic' - essentially, the way cells modify and read their own DNA.
Another possibility is an active jumping gene, or transposon: unlike most genes, transposons can move around in the DNA, and can sometimes carry with them a piece of DNA that tells nearby genes to be turned on or off (or are simply silenced by the cell, like in the PEV case above). If a transposon sits right near a pigment gene, it can cause that gene to be silenced. However, if the transposon up and jumps somewhere else at a random time (which active transposons do!), the gene nearby is no longer silenced, and can now cause pigment to be produced again. There's an example of this happening in snapdragons (see middle image). In this case, there is an actual genetic difference between the pink and white cells: one group has a jumping gene sitting next to the pigment gene, and the other doesn't.


Importantly, PEV silencing--like the transposon jumping--is inherited when cells divide, so if a stem cell that eventually makes a whole flower silences the pigment gene (or transposon jumps out), the whole flower will be white. If the silencing happens later in development, maybe when the early divisions forming the flower have happened, then a single petal, or just a sector of a petal, could be white, and the rest pink. Such sectoring is a telltale sign of PEV or transposon-related effects.

In your photo and description, the tree is mostly white, and individual sectors are pink, not vice versa. If the cause of the color switch is PEV, then the pigment gene's 'default' in this tree being silenced, with the silencing randomly moving away from the pigment gene in some cells. Or there could be a particularly active transposon that tends to bring gene silencing along with it at play here.