The straight forward method for hybrid gene seed is simple in concept, and in a less conspicuous form it happens all the time. Marines have a separate zygote for each organ, and a hybrid marine is just made by using zygotes from one donor marine for some of their organs and zygotes from a different marine for the others. "When mature, each gland contains a single gene-seed corresponding to each zygote implanted into the recipient Marine. Once removed by surgery, the progenoid must be carefully prepared, its individual gene-seeds checked for mutation, and sound gene-seeds stored."
The type case is Honsou the half-breed. He is an iron warrior with some gene seed from the imperial fists. Each organ is grown in a lab from its zygote, and at this point, especially for the iron warriors who are based on the daemon planet medrengard, that some of those organs will not be viable due to mutation. So, when making a marine it may be necessary to have some back-up organs ready for implantation, so it's possible that due to the number of back-ups required, stolen imperial fists gene seed could be used.
It must be more common, however, for the back-up implant to come from a marine of the same chapter/legion. So if a single Ultramarine's progenoid is harvested, and all its zygotes cultured to be implanted into an aspirant, that somewhere along that process of zygote to culturing to implantation, one or two organs will fail, and need to be replaced by one from another ultramarine. This seems routine, and results in an unremarkably "hybrid" marine.
Then there is a slightly more noticeable form of hybrid. Say the mechanicus were making a successor to the Black Dragons. Some of the black dragons have bone blades projecting from their bodies, which we can assume come from a mutation in the ossmodula. Perhaps however their other organs are exceptionally pure and a chapter is being made to exploit those organs. Regardless of which primarch is theirs, supposedly it's Vulkan, we know that none of the first founding legions have bone blades, so there exists a normally functioning ossmodula that the black dragons' ossmodula is descended from. If the dragons are descended from the Salamanders, it should be simple to implant an aspirant with eighteen Black Dragon organs and one Salamander ossmodula, creating a definitely "hybrid" marine, since we know from the mutation that black dragon geneseed is identifiably different from salamander geneseed, but they have been combined in one body.
This is also how hybrid chapters are made, since the gene seed for a new chapter always comes from a single, hybridized marine, even if it is the Ultramarine/Ultramarine type of hybrid describe above. “A single suitable gene- seed must be selected for each zygote. Zygotes are then grown in culture and implanted into human test slaves.... From the original slave come two progenoids, which are implanted within two more slaves, from which come four progenolds and so on. it takes about 55 years of constant reproduction to produce 1000 healthy sets of organs.“ From this it is indicated that when making a thousand sons successor, they may not find functioning Thousand Sons zygotes for, say, six of the organs. Ultramarine organs can be used instead, the full set of 12:6 Thousand Sons:Ultras organs can be implanted in a test slave, and then that ratio will be reproduced into 1000 marines' worth of organs.
Lost loyalist thousand sons who have appropriated some Ultramarine geneseed to keep their implantation rates up may have a more complicated issue if they choose to use the ultra zygotes on an as-needed basis and therefore have different levels of hybridization in each marine. However, I think it likely that if they have the opportunity they will experiment to find the most stable combination, since ad-hoc hybridization probably leads to greater levels of mutation down the road, as successive generations of TS progenoids have to reproduce random instances of Ultra organs.