Autocenter is a default effect playing on the device following power
up or reset. It is disabled by stopping all effects. On at least
some devices (all?) it is a spring effect playing in slot 1.
Capturing Windows USB packets reveals it dinput acquire does (1) a
reset (this enabled autocenter) and, if autocenter is disabled, (2)
a stop all effects (this disabled autocenter).

This logic works regardless of whether autocenter is a spring effect
playing in slot 1 or not. It does mean autocenter can only be set
when the device is not acquired. Testing on Windows reveals setting
autocenter properties while acquired returns DIERR_ACQUIRED even
if the device is exclusively acquired, so this is consistent.