Yes, it's normal - assuming I have interpreted your description correctly. The "soft-start"/5670 conversion kit eliminates that "pop". More significant, it allows you to adjust the driver bias for the best 2A3 operating condition.
There have been other approaches to optimizing that operating point, most notably a small resistor in series with the LED in the driver cathode (if adjustment is necessary). As a good approximation, the driver plate voltage should be close to 1/3 of the 2A3 plate voltage - this is what we specify in the kit.
The above only applies to the 2A3 (direct coupled) version.