It is best to think of an Electro Magnetic Pulse as a very short burst from a very strong radio broadcast. What happens is just like the radio waves from a broadcaster causing a small electric current in your radio antenna. Your radio or TV picks up those voltages and currents from the antenna then amplifies them to make the sound you hear.
The EMP creates a very strong set of current because the EMP device is much much more powerful than a radio broadcaster's station.
The voltage and currents it makes are strong enough to fry diodes, capacitors and especially transistors. Modern electronics are all chip based. Electronic chips are super miniaturized arrangements of capacitors, diodes, and transistors with some really fine transistors in the mix. Because they are so small they are much more likely to be fried by the high voltages and current than old systems with heavier components.
(We usually do not think about the chip having the same things in it as a normal circuit but cause they are all microscopic in size and sold as an integrated circuit chip.)

The EMP is normally short wave lengths too. The chips do not need to be connected to a proper antenna to fry. Almost any wire connected to them will do, even the line printed on a circuit board can act as an antenna. That is why they recommend placing radios etc inside a metal box. The hope is for the box to act as a Faraday cage and shunt the magnetic wave around the electronics.

EMP as a weapon is one of the great untried experimental weapon systems.
If anybody has tried using one they have never published the results.
Experiments with EMP which have been published are not totally convincing about how effective it would be.

Not all chips fry, not all radio tubes are immune.