Fission bombs can be tested with subcritical explosions. You have a plutonium core (a sphere the size of a grapefruit) and surround it with high explosives. Not as many as for an actual detonation. You blow them up, create the implosion, and trigger a subcritical fission reaction, or one that is very slightly supercritical. You then take lots of measurements (temperature increase, X and gamma rays, neutrons, etc) and see if they align with your theoretical models. If they do, you have extremely high confidence that the bomb will work as designed.

Now, virtually all nukes in the US arsenal have a fusion bomb stage too. The way that works in practice is this: you first detonate the fission component of the bomb, and that produces a huge amount of X-rays. It's so huge that the wavefront of the X-rays behaves like a solid hammer. That's what produces the compression for the secondary. This design is called the Teller-Ulam design, and it is extremely likely that it was discovered only once (by Ulam and Teller), all other thermonuclear bombs are just the result of successful spying and secret sharing.

This X-ray hammer can't be very easily tested. That's what these guys are doing.

Now, you may wonder if Putin's guys are doing an equally good job at testing their thermonuclear bombs. We don't know, but it doesn't make a difference: the fission part of the bombs is powerful enough to create utter devastation. The fusion part adds some extra punch, but it doesn't change the scale of devastation. And the CIA is highly confident that Russia is properly testing the fission bombs, even undergoing what is called "hydronuclear" tests, which, although not formally banned, other countries don't do.