As others have stated, most alarms that sound when the key is turned on and then go off, are related to oil pressure. If that is what your alarm does but is slow to turn off, then you may have an issue with your oil pressure. Most alarms are made to disconnect at around 6-9 PSI. Increase the engine speed to 1500 rpm
once it starts and that should shut off the alarm. If you have an oil pressure gauge, take a look at it although electrical
oil pressure gauges are prone to inaccuracy.
Some I/Os and outboards have a drive gear
oil LEVEL alarm which has nothing to do with the engine. Without knowing what you have for engines and drive systems, it would be a pure guess. Check the manuals
for the engines and drive systems.