A worry for quite a long time! People at the encrypted transmission service told me about that as I visited an embassy in 1975 or 1976. I didn't hear "Tempest" then, but they knew the weakness and tried to protect their data against it.
Which doesn't mean that the radiation could already be analysed then - only that they felt useful to take the possibility into account.
As for the Swiss experiment: most keyboards use contacts with high impedance, either because the contacts themselves are made by carbon-filled elastomers or because load resistors a big to reduce consumption, so I bet the contacts radiate very small (and indistinct!) fields, and the researchers picked data from the USB transmission instead, where keys are already encoded. The cable itself is more or less shielded, but the connectors not so much, and the electronics at both ends even less.
So put your aluminium foil rather there...
As for interferences, many of them can (and must!) be removed before analysing the leak by a keyboard. Though if your screen is a cathode ray tube, the attacker won't waste his time at the keyboard.