Probably will not hurt the fish unless the rate keeps up for more than a few minutes, perhaps 20-40 min.

If the other reg does not do that, you can upgrade to a better regulator.
My regs take awhile to fire the manifold set up.
I use the Victor brand which I think are the best.
Light duty is a decent grade.

About the best regulators here in the US anyway.
A needle valve might also be a point of error.
Clippard has a good track record and many use them, but admittedly, the Nupro and Swagelok brands are better.

Check valves also might be an issue.
How low is your CO2 tank pressure getting for this set up?

There are a few things you can look at if you can rule out the reg issues.
A cheapo Cornelis CO2 reg run about 20-30$ on ebay, Victors from about 30-60$.
Both can work well for many years.


Regards,
Tom Barr