The implant (theoretically) reduces the chances/growth rate of certain mammary/hormone related tumours. (It's done so with the benign tumours in my crew but not the less common malignant ones.) I don't know that this is even a mammary tumour (I also don't think it was a salivary gland tumour, that's what we think Amy had and it was in a very different location) and at this point, if it's regrown, it wouldn't be enough on it's own. (Tumours in young rats are especially worrisome and if they're regrowing this quickly even more so.)
The tumour (along with other medical waste) has to be disposed in a specific manner, so sometimes they still have the tissue in a fridge somewhere and it's worth asking. (It wouldn't matter if the rat was yours or the rescue's.) If it's not an abscess (I really hope it is), I would get it tested if you remove it. I don't know a lot about mammary tumours in males, but if it's mammary neutering or an implant may help reduce the recurrence/growth rate by regulating hormone fluctuations, but I doubt it would even be as effective as spays in females. (In my experience, spaying is so much more effective at reducing mammary tumours if it's done before a tumour has developed.)
I wouldn't give him Baytril just yet, you don't know he needs it and it can do more harm than good at this point. You can try doing a compress (I tried with Sophie but it didn't come to a head >() but don't be discouraged if nothing happens.
