3.1.67 opens this stretch of the Aṣṭādhyāyī, and its word सार्वधातुके — "when a सार्वधातुक [affix] follows" — carries on by अनुवृत्ति through every rule after it: 3.1.68 , through 3.1.81 , and the rest. Every one of the ten vikaraṇa is conditioned on exactly one thing — a सार्वधातुक ending is coming. Take that ending away and none of them are licensed to appear.
What counts as सार्वधातुक
3.4.113 — तिङ् endings (broadly), and शित् affixes: anything carrying a श् as its own इत्, which is most of the ten vikaraṇa themselves (शप्, श्यन्, श्नु, श, श्नम् all literally contain श्). 3.4.114 sweeps up everything left over — क्त्वा, तुमुन्, क्त, the future's स्य, the desiderative's सन् — and calls it आर्धधातुक.