For anyone who is really intrested in building multiplayer games on phaser using matter/arcade physics I can recommend the following server side lib/framework (nodejs) - https://colyseus.io/

As well, they have the tutorial for phaser example - https://colyseus.io/learn/phaser/

In that case all important calculations (like player movement etc) should be done on SERVER SIDE on each tick and the client side should visualize the updates.

Seriously, colyseus saved me a lot of hours and it's pretty simple!