That is not correct. The test/oath come from the "events office". Your application has a primary office, a secondary office, and an events office.
The events office is likely the one closest to you and will be the one scheduling your test and oath.
The primary office is the one actually processing the application. You can find this out by calling IRCC and just asking what your primary, secondary, and events offices are for your application. You can also find these on the GCMS notes.
Additionally, if you receive a fingerprint request, this has the address and email of the primary office at that time.
Presumably, the primary/secondary offices can change during your application, but the most up to date information can be determined by calling the IRCC Contact Centre or requesting GCMS notes via ATIP.