That definitely sounds like not you. DPS in low level content often ill realise that them pulling aggro from a tank is not a good thing - and it doesn't help that oftentimes tanks also don't realise that they're not being targetted by everything they need to be!

Medica actually only generates about 20% more aggro by nature than Cure, but neither generate all that much. That said, the main danger in Medica use - or wayward regen or medica ii use later - is more in the possibility that you're healing a target who hasn't really established aggro (eg an archer that's targetting a DPS when neither the DPS or tank has noticed). Given the situation though you didn't do that bad.

If you find yourself with aggro, for future reference, run yourself over to the tank. Assuming they aren't braindead (in which case, welp), the enemies that follow you should be noticed by the tank who'll pick them up quickly.
Disclaimer: Avoid doing this during bosses as bosses usually have high-powered cleaves that deal high damage and it's not fun. But for mob pulls this is generally best.