Fish parasites can only, by definition, be found in water which contains fish as otherwise they wouldn't be able to survive. On the other hand, Tubifex are only found in water that doesn't contain fish, it would be far too polluted for fish. Therefore, it's impossible to see how tubifex could harbour fish parasites or diseases. Problems appear to be caused when people have fed dead and decaying tubifex, but the same could be said for any live food if you let it die and decay.
Like you I fed fish on tubifex many years ago and am happy to continue today.