In any case, I find eSHa 2000 a much better anti-finrot and anti-fungus medication, so if you have the option, use that. Either way, medications based on formalin and organic dyes generally work much better than tea-tree oil, so the latter can be dispensed with.
Unless you're an doctor or a vet, using multiple medications to "cover all the angles" isn't wise at all. Medications are designed to be used on their own. In combination, results are unpredictable. Always remember medications are poisons, and the idea is to use as little as possible, and only when completely necessary.
In the case of finrot, an antibacterial medication should work fine. Adding tea-tree oil is redundant. Tea-tree oil does nothing that antibacterials or antibiotics don't do, and there's a very strong argument tea-tree oil does those things much less effectively than either antibacterials or antibiotics. That's why, when humans have gangrene, which is what finrot is equivalent to, the doctor doesn't reach for tea-tree oil, but an antibiotic.