Nuclear chemistry home made
Yes, this really happened, probably (it's not a peer-reviewed effort).

The reactor is a Farnsworth fusor, a very low-density, low-rate inertial-confinement reactor. They're surprisingly easy to build and get working; many people have done so, and verified their function by measuring neutron output. An accelerating voltage of 10 or 20 kV produces particle energies equivalent to over 100 million degrees C.

There's active debate about whether a fusor of this design could ever produce more power than it consumes, but there's been some interest in using them as compact neutron sources (that you can actually switch on and off).

You asked about fusing hydrogen-1 to hydrogen-2. These experimenters don't attempt that; they just buy deuterium, which is also readily available.