Changing tempo can result in a mess until one gets their head around musical timebase vs. linear timebase.
The first thing to keep in mind is that although musical timebase sounds an awful lot like “musical mode”, they are completely different functions! It’s not uncommon for people to use one term when they mean the other, so when reading explanations and posts, it’s important to stop and decide whether the poster is using the correct term … otherwise things make no sense at all and can get very confusing!
Back to musical timebase vs. linear timebase: It’s critical to have the right timebase chosen on each and every track before changing tempo, otherwise things will probably wind up playing at the wrong point in the project. (BTW: a nice feature in Cubase 9.0.20, going back as far as Cubase 8.5 or earlier possibly, is a Project Logical Editor setting to toggle all the tracks’ timebases).
For example, if you have a track (audio or midi) with multiple segments (pieces of music set along the track), and it is set to musical timebase (the orange quarter note icon), when you change the tempo and play the track, all the segments will START at the same BEAT as they did in the original tempo.
On the other hand, if your track with multiple segments is set to linear timebase (the gray clock icon), when you change the tempo and play the track, all the segments will START at the same TIME (as in minutes:seconds) as they did at the original tempo, but of course that means that the starting beat of each segment will be different than it was at the original tempo.
One last thing, regarding visual “shifts” on the screen when changing tempo: whether the music “shifts” visually on the display when the tempo is changed depends on not just which timebase the track is set to, but also whether the ruler display is in bars:beats mode vs. minutes:seconds. For example, if the tempo is changed with the track in musical timebase, and the ruler display is in bars:beats mode, there probably won’t be any “shift” apparent on the screen. But if the ruler is in minutes:seconds mode, there probably will be a visual “shift”.
Conversely, if the tempo is changed with the track in linear timebase, and the ruler display is in bars:beats mode, there probably will be a visual shift of the musical bits on the screen. But if the ruler is in minutes:seconds mode, there probably won’t be.
So what is Musical Mode? First of all, it applies to audio only, not MIDI. Next, unlike Musical Timebase, it doesn’t apply to tracks … it’s not possible to put a whole track in Musical Mode. It applies only to individual sections of audio on the track. It’s easy to tell when Musical Mode has been activated on an Audi segment - there is a little squiggly line at the top right corner of the segment (sometimes only visible after zooming in).
What does Musical Mode do? Consider what happens to a piece of audio when the project tempo is slowed down 10-15 BPM. All the MIDI in the project plays back great from the start of the song at the slower tempo. Then you get to the piece of audio, and it is completely out of sync … it plays back at the original tempo!
The way to have the audio play back at the slower tempo is to place it in Musical Mode (before changing the tempo), this can be done by checking the Musical Mode box in the Pool (CTRL-P) for that specific piece of audio. Then everything sounds great, all MIDI and audio in sync at the slower tempo.
Hope that helps a bit. There are sections in the documentation dealing with this (or there used to be in the .pdf version, I haven’t checked to see in the on-line version), and that may help as well.