Client animation played on server but not on client

I’ve replaced the default third person character animation with my own animations, I have set up all states and rules for transition. They work fine on server side. However, the client side didn’t get the update of itself although client side indeed got the update. For example, when starting the game, both client and server are on Idle state and thus will play Idle animation. When pressing W the character will move forward, and if I move the character on server side, client got the update, if I move the other character on client side, server got the update. However, when I press W and Shift at the same time, the character is supposed to run and thus play the run animation. When I press buttons on server character, the animation plays fine on both client and server side. But when I press buttons on client character, the client didn’t play the animation but the server played the animation correctly, although the functionality on client side indeed achieved even though the animation is not played.

This is my locomotion graph containing states and rules for transition:

This is the “Idle” state, the rest states are similar to this one:


This is the transition rule from Idle to Run, the rest rules are similar to this one:


So what can I do so that the client side can get update of itself? Thanks.