There are two problems of Advanced Tesla coil and HeroTurrets mod. Probably more appropriate place to post this on the Heroturret page, but the author is not responding, and may be you could take a look:

1) A tier bagde of a heroturrent level is hiding inside the Advanced Tesla coil texture in the world.

2) if you change in the settings of the heroturrent, the Killcount to be not "fizzy" but specific, then in the gui of all logic prototype (for example the requester chest request menu), every tier of Advanced Tesla coil appears twice, while all levels of default towers appear once

Well, I am no longer a user of hero turrets. Its a neat concept but did not have large enough impact on my gameplay to justify it. Maybe I will take a look into this if I have some time to kill, but no promises on my part.

BTW besides what you mention, I don't think hero turrets is a good fit with this mod even if the aforementioned problems are corrected. This is because a lot of the damage the coils do come from some sort of 'effect', like an additional explosion or from connecting chain lightning. These effects are implemented in a somewhat hacky way involving other 'helper' entities. this means that most of the times the actual kill does not belong to the turret but to these 'helper' entities. You can check the kill count of the turrets. they creep much slower than how much bug is being stomped.

Effectively this means that they will level much slower than they should.