A good way to check if your lagging is to check your ping by pressing Alt + F8. If this is a new creature to you and your not sure of their behavior it can be quite confusing. Creatures can have different abilities and behavior, some that we can't even calculate or can be quite random it all depends on the creature. I do know as soon as you engage with a creature it will begin to use spells. Some creatures run away and actually can haste or even charge at a certain hit point, typically deep red. A good example of this would be Nightmares or Minotaur Hunters. It is indeed a monster behavior, and every monster is different. My suggestion to you would be to name the creature your hunting here or you can look up your creature on Tibia Fandom for example to see it's behavior and abilities.
Also, if you're suffering from lag please see this question: How to fix lag and improve in-game latency
A good tip about the lag would be to check your options!
Click Show Advanced Options then Options->Misc->Optimise Connection Stability.