My spouse and I are jointly filing. On the "File" tab, Turbotax instructs me to submit to the CRA under my name or my spouses name. I chose my name. Did both get sent?

You can't file jointly in Canada, only prepare jointly. I do wish Turbotax would make that clear!
Everyone must file individually, so you must transmit each person's tax form to CRA and receive separate 6 - digit confirmation codes from NetFile. It is not an either/or situation, both returns must be transmitted.