Steps to reproduce:

1. Open attached project and build it

2. Run 4 instances of project. (Let's call them "Client_A", "Client_B", "Client_D", "Server")

3. Run "Server" as Server Only. Scene will changed and you see 3 "jumping" blue boxes. They are "jumping" cause of blending 2 animation by parameter "axis" (look for AnimatorController asset in project). Blue color represents Server controlled objects

4. Run "Client_A" , press "Connect" button. Scene will change, and you see 1 green box, and 2 jumping red boxes. Green represents your client controlled box. Red - other clients. By changing Vertical axis (UP, DOWN arrow keys) you change the "axis" Animator's parameter, and your box starts jumping. When "Client_A" connects server, on server scene one of the boxes became White - it's mean that some client controlling it

5. Run "Client_B" , press "Connect" button and you will see similar situation. 2 red and one green. Green is yours. On Server on of blue boxes became white

6. Run "Client_D" , press "Connect" button. 2 red and one green boxes again. On Server now all the boxes are white

7. Now all preparations are done, you can control any client, to see if boxes are syncronized

8. Do not change Vertical axis on "Client_D" and disconnect it by pressing stop button. On Server one of white boxes became blue, and starts jumping (it means server assing parameter "axis" on Animator of Client_D's box). On "Client_A" and "Client_B" - that box does not jump (though it should)

9. Disconnect "Client_B", and Connect it again. Notice that "Client_D"'s box now is jumping.

Reproduced with: 5.3.2f1, 5.3.3p3, 5.4.0b10
5.2.4f1 had different bug regarding NetworkAnimator so couldn't check there