Hi,
First off, I haven't worked on one of these so I could be completely wrong. Please keep that in mind.
But here's my 2 pennies worrh:
If you are asking about water coming up into the engine mount case from the upper shift shaft, that's probably not so good.
There is a rubber grommet that the water tube fits in (item 14 in the link below) and it sounds as if you may have missed it when putting the gearcase back or it is missing/damaged. Getting that tube reinstalled correctly after it's been disturbed is tricky for sure sometimes. And, I believe that the grommet gets mangled and pinched when you miss.
I know from other old outboards that I have repaired that a damaged/deteriorated grommet is not unusual and that can also mean that the hole for the grommet can be eroded or wallowed out from water pressure or the water tube banging around.
I have fixed a few by applying and shaping epoxy to reconstruct the hole so that the grommet will fit and stay put but it's always required removing the powerhead.
Buy OEM Parts for Honda Outboard 30HP OIL PUMP Diagram
www.boats.net
I see there is a grommet for the water tube that fits into the extension case. I'm not sure why that's there but it could be to hold and help align the tube. Like I said, I'm less than a rookie on one of these models.
Here's where you can buy a legitimate shop manual if you're interested:
publications.powerequipment.honda.com
Expensive but usually well worth it to the DIYer
Good luck.