To be honest, I haven't really fought any good Tinks before. I tend to treat him like a more mobile Link with slightly worse range, but the Tinks I've played weren't really high-caliber and it's been a while, so it's hard to remember if I do anything significantly different in neutral compared to fighting Link.
For edgeguarding, it's hard if they have a bomb because they can not only AGT for a boost, but they can also throw it at you. If they're recovering at stage level, then I recommend grabbing the edge for invincibility to get through the bomb. At this point, they'll forced to either up+B or tether; Tink's up+B is more dangerous than Link's in the sense that you can get stage-spiked or sent in an edgeguard position if you mess up, but I would recommend grabbing the edge and using the invincibility frames to protect yourself as you go for an edgehop BAir. If you read an airdodge -> tether, then you can try baiting out the airdodge and then BAir'ing them immediately after their invincibility when they try to tether. In the case that you edgeguard Tink from on-stage and they try to tether, you can usually walk-off DAir or FAir after you see the airdodge and hit them as they initiate the tether. Tink's up+B may also be easier to edgeguard from on-stage since it provides relatively little coverage above his head; you can probably go for either a DAir spike or weak DAir -> BAir. Again though, I haven't played any Tinks lately, so that's building off of Link experience and past memory.