Understanding UJT relaxation oscillator
The key point that you're missing is that R1 has a much lower value than R3. Before the UJT conducts, all of the current through R3 goes into charging C1. But once the UJT conducts, R3 and R1 form a voltage divider that produces a much lower voltage. This is why C1 discharges through the UJT and R1. When C1 reaches that voltage, then the UJT stops conducting and the cycle starts over again.