You're definitely looking for the "Join" recipe.
* Add first your "time series" dataset
* Then add your "profile" dataset
* Select customer id as the join key
* In the columns selection, select all columns from the time series table and the additional columns that you want from the profile
Assuming that there are no duplicates in your "profile", a regular ("inner") join will work.
The output will contain one record per record in the "time series" dataset, with added customer profile info.
Hope this helps,