This is up to the DM:

As noted in PHB 198 (emphasis mine)

Monsters and Death

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws. Mighty villains and special nonplayer characters are common exceptions; the DM might have them fall unconscious and follow the same rules as player characters.

Depending on how your DM rules he could say that it is technically an NPC/Monster even if you control it most of the time. Or he could say it is an extension of the player character and thus follows the same rules. Bottom line is you need to ask them.

This is up to the DM:

As noted in PHB 198 (emphasis mine)

Monsters and Death (in this case player controlled monster)

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws. Mighty villains and special nonplayer characters are common exceptions; the DM might have them fall unconscious and follow the same rules as player characters.

Depending on how your DM rules he could say that it is technically an NPC/Monster even if you control it most of the time. Or he could say it is an extension of the player character and thus follows the same rules. Bottom line is you need to ask them. It would be unlikely that he/she would not allow them to follow the same rules as the players as they usually become part of the party, like a mascot.