ah wait, actually the moment either side wins +1 the other side (everyone except the attacker) should switch to that tip, unless attacker can prevent or slow down propagation until he has a competing block ready,
Consider what it takes to reach the lock-in depth:
| Step | Chain A | Chain B | Lead | What must happen to continue |
|------|---------|---------|------|------------------------------|
| 1 | 101 | 101 | Tie | — |
| 2 | 102 | 101 | A +1 | B must ignore A's lead, keep mining |
| 3 | 102 | 102 | Tie | — |
| 4 | 102 | 103 | B +1 | A must ignore B's lead, keep mining |
| 5 | 103 | 103 | Tie | — |
| 6 | 104 | 103 | A +1 | B must ignore A's lead, keep mining |
| 7 | 104 | 104 | Tie | Depth 4 reached, lock-in |
Each "must ignore" step is a deliberate choice to deviate from default policy.