Hello

In our SharePoint 2013 farm we use the User Profile service applications very heavily.

I want to change the server that is hosting the service. The User Profile service application which is currently running on: (Server-1), But, I want it to be running on: (Server-2) instead.

Is this (https://technet.microsoft.com/en-us/library/ee704549.aspx?f=255&MSPPError=-2147217396) the right/proper way to do it? What about the order?

I mean: Should I go to: Manage services on server > Server-2 > Start: User Profile. 
After that: Manage services on server > Server-1 > Snbsp;

Or, The other way around:

I mean: Should I go to: Manage services on server > Server-1 > Snbsp;
After that: Manage services on server > Server-2 > Start: User Profile. 


Or, Is it a totally different way? Does the same way apply on other service applications too e.g. Managed Metadata too ? 

I am asking about this because I really want to be super cautious while doing this change to avoid crashing the service or corrupting it.

Thank you !

Yes, that's correct.

But Trevor, What about the order? 

Start it on the new server, then, stop it on the current one.

Or

Stop it on the current server, then, start it on the new one ?

The order doesn't really matter if you're quickly doing this, but you could start it on the new and stop it on the old.

User Profile Service should generally run on the 'WFE(s)' since it is an end-user facing service.