On all the conventional powered diesel tugs that i have been on including CP systems, there is no instantaneous reverse, as you have to wait for the engine revs to slow down to enable the gearbox cogs to mesh and then there is always a built in delay of 15 to 20 seconds, before the change of gear actually happens. For emergency crash stops there is a system which crashes the gearbox astern, but that is for emergencies only the high engine revs could probably damage the gearbox, the system is usually tested at specified periods by an engineer and the engine is usually at low revs. Though on small and medium tugs I have been on it does not exist.
Voiths and aqua-master systems you can go immediately ether way as the engine revs are always constant. Also steam recip can go astern immediately.