First off this is called genetic mosaicism and indeed mitotic recombination is a contribution factor.
Mitotic crossover events involve the exchange, by homologous recombination, of regions of chromosomes. 60% of homologous recombination events might occur during G1 and 40% of those event occurs after chromosomes are replicated (see this paper). For twin spotting to occur, you need the homologous recombination to happen on replicated chromosomes (i.e. you need 4 chromatids).
For you question on twin spotting. The following picture illustrates well what are the outcomes of homologous recombination involving two alleles and replicated chromosomes (each line being a chromatid).
If the cell is heterozygous (normal phenotype) for the two recessive alleles, here called y and sn (respectively the "yellow" and "singed bristles" alleles), then two recombination scenarios are possible and differs based on where the recombination occurred. Note that y+ and sn+ are the wild-type alleles and carrying those alleles do not provoke a particular phenotype. The phenotype of the resulting daughter cells are:
- Twin spots: Yellow but not singed spots (y/sn+) and singed but not yellow spots (y+/sn) for recombination after the y/sn locus
- Single yellow spots: Yellow but not singed spots (y/sn+) and no spots (y+/sn+) for recombination between y and sn
Here the actual picture of what happens:
Therefore this should make clear why daughter cells can show phenotypes that differ from the original parent cell, i.e. the combination of alleles (especially for recessive ones) changes after mitotic crossover events. The twin spot phenotype in Drosophila melanogaster is an excellent example for illustrating that.