I think the problem you’re having is that you’re moving the player with a player controller (scripting, etc.) and then you are trying to change his position via animations from your 3D package. This is why you are having these issues.
I recommend for you not to use animations from your 3d package to change the position of the entire character in your scene/level. You need to design something much more robust for in-game character re-positioning. You 3d package should only concern itself with animations that supplement player aesthetic movements, like talking to another character, punching, etc. Unity via scripting, character controller, etc. should be in charge of your character’s position in the environment space.
Here is an example of how I would approach making a player walk up to a ladder, climb it, and then get to top/complete the ladder climb:
1- make 2 player triggers, waypoints, helpers, whatever you want to call them; one for the bottom of ladder and one for top; basically both ends of the ladder.
2- setup some code so when the player walks up to this trigger and hits the “climb ladder” button to initiate some function, this function can make the player controller get constrained to a rail type system where if the player hits the move forward button, player controller moves up the ladder at a set speed, but if player hits walk backwards button, player climbs or moves down; sideways movement should be constrained and not available while this function runs. When player reaches the top, another trigger can activate the end of the action, allow player to exit “ladder” mode and continue on, etc.
3- setup the animations in your 3d package; synchronize your animation to match with the ladder geometry you also make in the 3d package; this takes some careful planning and attention must be paid to scene scale, which should match with your Unity environment. This part basically takes care of itself, considering you did a good job when planning and writing your technical design document, etc.
4- make it all work in Unity; make the triggers/ladder endpoints work with the player controller movement, and add animation from the 3d package, which will complete the aesthetics part of the player action- done.
Keep in mind, this is just one way of engineering this feature for your game, there are probably 101 ways to go about this. I would recommend going to the drawing board and doing some planning and wireframes of this feature and narrow it down to a method you think will work best for your game. A properly engineered plan will make all the difference here, and in every aspect of game development. Good luck.