roboticus is exactly right. If your tables are identical, you can use the same DBIC schema/model for every account, just supplying the correct connection credentials to get the right DB. Dynamic schemata are quite limiting (no many_to_many auto-discovery) and a performance hit. Per user connections are possible but not the default so you'll have to hit the docs and maybe the mailing list. I've never done it or I'd give a link/example.
Sidenote: DBIC (DBIx::Class) is not Catalyst and does not ship with Catalyst and Catalyst doesn't tie you to any DB or model at all.
Update: strangely enough I came across this today in looking for something unrelated. Though I've never used it, it looks like what you want if you're running DBIC in Cat: Catalyst::TraitFor::Model::DBIC::Schema::PerRequestSchema.