score:4
Other than Suleyman's notorious short temper and tendency to keep grudges against people who caused offence whether real or imaginary, With further reading, it looks like that It wasn't Suleyman that the Generals personally disliked, rather his alliances.
For context, Umayyads themselves were Adnanite Arabs (Qaysids) but Princes and Caliphs often allied themselves to Qahtanite Arabs (Yamani) for political benefits. The historical rivalry between the two factions was described as harmless before Muawiya I of Umayyad Caliphate but it became violent when Marwanid branch of the Umayyad dynasty rose with the support of the Yamani faction and Hashimid claimaint Abdallah Bin Zubayr clashed with them, supported by the Qaysid faction. Umayyads triumphed and the new Caliphs strived to keep a balance between their erstwhile supporters (Yamanis) and newly reconciled subjects (Qaysids). Both factions however carried on sporadic raids on each other to settle their accounts as late as Caliph Abd al-Malik's reign who settled their complaints either by paying blood-money or by issuing warnings to the aggressor party. His reign is when the Qaysid's became allied to Abd al-Malik's brother Muhammad ibn Marwan whereas Yamanis allied themselves to his son, Suleyman who was at that time governor of Palestine. Yamanis also courted other Umayyads like Umar bin Abd al-Aziz who eventually succeeded Suleyman as Caliph.
Now fast forward to the timeline in question, Caliph al-Walid's mother was a Qaysid Arab noblewoman from Banu Abs clan which is why Qaysid generals like Qutayba (Belonging to Qaysid Bahila Clan), Hejaj and Muhammad bin Qasim (Both belonged to Qaysid tribe of Banu Thaqif) supported him. Musa Bin Nusayr's tribe is contested, some claim he was a Lakhmid (Yamani), others claim he was a son of Banu Bakr confederation (Qaysid). If he was a part of Banu Bakr, it would make sense that why would he be more loyal to al-Walid and his sons rather than Sulayman who, despite his Qaysid mother's heritage, had allied himself to the Yamani during his term as Governor of Palestine. Tariq's situation is also disputed. Some say he was a part of Yamani Kindah tribe, other say he was not an Arab at all but rather a Berber. In any case, Musa and Tariq do not seem to be as outspoken in their opposition like Hijaj and Qutayba, nor did they rise in rebellion afterwards like Qutayba. Their only offence appears to be subtle act of defiance shown to Suleyman in last hours of al-Walid.
Yazid ibn Muhallab on the other hand was part of the Azd tribe which was a part of the Yamani faction, so he naturally supported Suleyman as opposed to the claimants favoured by the Qaysids. Suleyman was their guy whereas his nephews were the enemies. Suleyman knew that he was very unpopular among the Qaysids which is why he did not move to Damascus even after becoming Caliph and remained in Palestine where his Yamani support base was strong. The reason why the Army seems to be stacked against Suleyman is because it was dominated by Qaysid faction under the reign of Caliph al-Walid. Caliph Suleyman's purge however changed the situation in favour of Yamanis.