Nice to hear that everything is working, but the 12V supply is not really recommeded. A 9V supply is preferred. The amount of power that the 7805 has to dissipate depends on the voltage drop from the input (12V in your case), minus the target voltage (5V). This results in a lot of power being wasted.
The 7805 can handle it, but it should have a heatsink if you want to continue using the 12V supply.
A more modern solution is to use a buck converter, but the soldering needed for these is slightly more difficult, and so we only put buck converters on "more advanced" kits. The 5 pin TO-220 is a bit tricky to solder. It has 5 legs in the same space as the 7805's 3 legs.
If you use a heatsink: Do not mount both the 7805 and the MOSFET on the same heatsink without insulating them. The metal tabs are connected internally, and you will have trouble if you try to mount them both on the same metal heatsink.
Got the 9V supply today and was able to alleviate the problem. The 7805 still gets warm but it doesn't get too hot to the touch. I did have comments of other Nixie clock creators that in their case the regulator hardly gets warm at all though.
And I'll get a few buck regulators anyway. A more efficient clock is never a bad thing.