The deflection was magnetic, not electrostatic because of the wide deflection angle needed.
The vertical (field) deflection was done with something much like an audio amp driven with a sawtooth signal, except that the feedback was taken from a current sensing resistor in series with the deflection yoke. At this low frequency the coils behaved much like a speaker, having mostly resistance but some reactance. Hence the current in the coils was an accurate sawtooth, but the voltage across them was a somewhat distorted sawtooth due to the inductance.
The horizontal (line) scan at 15kHz could not be done that way because the coils had too large a reactance, in fact they behaved like a near-perfect inductor with minimal resistive loss. To achieve flyback in a reasonable time called for a large voltage, typically 1200v, to be applied for a few microseconds.
The way this was achieved was similar to IC engine ignition - the primary of the flyback transformer (or choke, as far as the scan circuit was concerned) was connected across the DC supply by a special high voltage transistor such as a BU508, the current allowed to build up, then the circuit abruptly opened. The sudden collapse of the magnetic field in the transformer created a large voltage spike, the flyback voltage. This was applied to the scan coils via a capacitor, and caused the spot to rapidly return to the LHS of the screen.
The forward scan drive required nothing more than a fixed voltage to be applied to the coils. Remember they behave as a near perfect inductor, hence with a fixed voltage applied the current, and hence deflection, would rise at a near linear rate. This forward voltage was provided by the charge induced on the series capacitor during flyback.
Consequently the scan waveform looked like a half-sine pulse a few microseconds long, of ~1200v amplitude at the end of each scan. You needed a x100 probe to scope it - a x10 probe could fail as they are typically not rated for that voltage. The DC scan voltage was not greatly noticeable due to its much smaller value.
-and no, the BU508 was *NOT* driven with a sawtooth waveform. It was driven with a square wave of slightly more than 50% mark to space ratio.
Why >50%? Because it also served as a return path for the scan current on the second half of the scan. On the first half the current was in a negative direction and was carried by the reversed C-B junction. Or, by a separate diode. The second, positive, half of the scan current required the transistor to be already on when it commenced.
As with SMPS practice today, the BU508 had to have a fully saturated 'on' interval and a clean, sharp switch-off otherwise it would dissipate substantial amounts of heat due to resistive loss. When the transistor failed repeatedly (in spite of no obvious picture symptoms) it was usually because of a driver stage fault giving weak base drive.
The scan voltage was the one to really watch out for, safetywise. 25kV EHT could give you a painful zap, but it was usually just that. A kilovolt at a substantial current could terminate your existence. Period.