D&D lore suggests that the demon usually hates who summoned them\$^1\$, this is confirmed in Demon Summoning paragraph in MM (page 51), emphasis mine:
Demon Summoning. Few acts are as dangerous as summoning a demon, and even mages who bargain freely with devils fear the fiends of the Abyss. Though demons yearn to sow chaos on the Material Plane, they show no gratitude when brought there, raging against their prisons and demanding release.
Those who would risk summoning a demon might do so to wrest information from it, press it into service, or send it on a mission that only a creature of absolute evil can complete. Preparation is key, and experienced summoners know the specific spells and magic items that can force a demon to bend to another's will. If a single mistake is made, a demon that breaks free shows no mercy as it makes its summoner the first victim of its wrath.
In the situation described (there are no more enemies and the CHA saving throw is successful), if the summoner has not attacked the demon then the latter can not directly attack the summoner due to the spell description
If you issue no command, it spends its turn attacking any creature within reach that has attacked it.
but they may try to gain some advantage on them, waiting to break the spell and then be ready to kill them.
If the demon breaks free and the summoner is unprotected (outside of the protection circle drawn for the casting, for example) the quoted paragraph from the MM says that the demon will firstly attack its summoner.
\$^1\$ See for example when Cadderly Bonaduce summoned an Imp or the Balor Errtu in the novel Passage to dawn.