Your firmware is base on the amount that the cable company is going to throttle your speed/demand on the loop you are connect to, and why the updates/firmware is done by the cable company instead.  So the question comes down to who your carrier is, and if they push updates to modems, of if you have physically take the modem to them to update the firmware when needed instead.

Comcast will push the update over the internet, while TWA does not.

And no, Motorola doesn't release firmware updates to the public, so don't bother trying to looking for such.  The updates are carrier specific, and why its the carrier that will do the updates when needed instead.

When you swapped modems, the new modem should have not worked until it was registered to your account (with the old one deleted).

This should have just taken a phone call to your internet provider to clear your account of the old modem mac address first, then plugging in the new modem doing the standard first time log into the provider to register the new modem mac address to the account next (or you give them the information over the phone and they can insert it that way instead).  During the new registration of the modem mac address to the account, this is when the provider will push the needed firmware to adjust the speed of the  new modem being registered to your account for what you are paying for.

As for if you think that the firmware is well outdated, then just do a hard reset on the modem to set the firmware back to factory, turn the modem off, then back on and let it reconnect to the provider.  During the initialization of the modem to the provider, it will flag that the modem needs updated firmware, and the firmware will be updated automatically on the initialization to the provider.