Always consult the Owners Manuals
From Axe-Fx II Wiki
What is spillover
Spillover is a processor feature where the trails of a delay or reverb can still be heard after switching to another sound.
All FAS processors support spillover, under certain conditions which are explained in the manual.
Spillover is enabled or disabled across all presets in the Global menu. Note that enabling it still requires additional steps to make it work, as explained in the manuals.
This parameter affects preset only, not scenes.
Scenes and spillover
The Global Spillover setting doesn't apply to scenes. Delay and Reverb trails are always carried over when switching scenes, depending on the effect block's On/Off state and its Bypass Mode setting. This is inherent to the way scenes work.
Scene controllers give you more control over what happens with the sound when changing scenes.
The Multi Delay and Megatap Delay effects don’t support spillover between preset switching.
Spillover can be affected when switching between the X/Y states or channels of an effect, if drastically different algorithms exist between the two states. For example, if one scene has a Digital Delay and the next scene uses a Tape Delay, spillover will probably not function correctly as these modes use different algorithms.
Forum member: "I have two patches that both has delay blocks disabled and when I switch between these patches via MFC the delay spillover sometimes kicks in really loud."
"This can happen if you rapidly switch between presets many times. The unit requires a small amount of time between preset changes to clear unused buffer space. This is done as a background task." source
If you use the Mix and Level parameters to dial in the desired effects level, the volume level of the reverb and/or delay trails may change when switching presets. This can be prevented by keeping Mix and Level at fixed values, and using Input Gain to set the desired effects level. source