yes it is common for alters to be talking and doing things when people with DID dissociate. thats what the disorder is all about...

having two or more alternate personalities that take control and do their jobs, purposes, reasons for being created in every aspect of the DID persons life. you can read the actual diagnostics wording on this in the link at the bottom of my post. please note though this is the american version of the diagnostics. your location may go according to other standards and definitions.

my suggestion is contact your (or a) treatment provider in your off the computer location. they will be able to tell you if this is normal directly related to you, your problems and your locations standards of what DID is, alters and such.