Things are complicated, and I usually don't know every aspect, but if a team has a players "Bird Rights", which should be the case for both Horford and Kornet, they can exceed the salary cap or other thresholds to resign their players. Some teams are hard capped and this would not apply to them. For example, if a team used the non-tax MLE to sign a player, that could result in a hard cap for a year. If there is a hard cap, the team cannot exceed that. The Celtics are not hard capped.
For Horford and Kornet, it comes down to what other teams would be able to pay, more than what they might want to pay. Most contending teams are over the salary cap so they would have to use an exception to pay more than the minimum. If teams are over the 1st apron, they can't even use the exemptions. I don't think either Kornet or Horford are going to see big offers from other teams but Kornet in particular is likely to have offers above the minimum that he is making now. The Celtics are very likely going to have to give Kornet a raise to keep him. Horford is at $9.5M, which is pretty good for a 38'ish year old who only plays 60 or so games per year. I could see him accepting a little less per year moving forward.
Again, the key is that a team must be under the 1st apron in order to be able to use their MLE. A tax paying team can only use $5.7 of the MLE and if they use it, they would then be hard capped at the first apron. This is why I expect that the market value for Kornet or Horford would probably be around $5M. This is the most that most teams would be able to offer. And even with that, most teams are not going to want to hard cap themselves for Kornet or even Horford.