I don’t know, you have to decide that for yourself. If you didn’t do anything wrong, there’s not really a reason to tell them anything, but if you’re worried and want to contact them about the misleading testimonial and are confident that you can prove that you didn’t do anything wrong, to clear that up preemptively and you think that’s a good idea, go ahead. Nobody here can decide that for you.
If you know him from discord, talked to him on discord, and asked him to order from you on Fiverr, that’s fine. If you told him to talk to you about the Fiverr order on discord after he ordered from you on Fiverr, that might be a problem, since typically, unless your profile or gig is approved for anything else, any communication regarding an order has to happen on Fiverr.
Talking about feedback with buyers, as you must have done, else he wouldn’t have admitted to having made a misleading testimonial, in and of itself is problematic, since sellers aren’t supposed to discuss reviews with buyers, there are many forum posts that warn against doing so.
If support looks into this, you can hopefully prove your statements; if your Fiverr chat doesn’t show that you told the buyer to talk about things in discord, after they had ordered, it might be fine, that would support the claim that the buyer’s feedback just was unfortunately worded, however, discussing reviews with buyers itself can also lead to warnings, so be careful with what you do.
The only thing I can tell you with certainty is that if you didn’t communicate about the order on discord with your buyer after he placed the order on Fiverr, then, no, you didn’t break ToS in that point.
Fiverr does want sellers to bring in new customers from elsewhere, after all, just, once you do so, you should stick to Fiverr rules, to avoid such issues.
Let’s say I have a friend I use to chat to on Discord, and they happen to need something I offer on Fiverr. I’ll ask them to order my gig there, no problem. From that point on, in regards to that order, I’ll only talk to them on Fiverr to avoid any ToS conflicts. Of course, I’d still chat with them about Final Fantasy 14 or whatever on Discord, as before, but anything to do with the order they made on Fiverr has to happen on Fiverr. I’d probably also tell them that before giving them the link to order, to make sure that’s clear and I won’t run into trouble later.
Your situation there, with already two prior warnings, is a bit complex, nobody can tell you how it would go, depends on what you can prove/what Fiverr would find when looking at your chat logs, and probably also on the person handling it and your prior warnings; if they were for the same or a similar issue, that’s probably worse than if they were for unrelated things.