After 30 days, the charm affect ends in an awakened creature or plant; it says, they will determine based on how you treated them if they like you or will stick around. Should that be a roll, or should it be purely based on how they were treated? For example, an abused homeless animal was awakened, treated with respect. fed well and given power to protect itself/get revenge if it desires, no expectations, just support, would it roll to determine, or be automatically cool with you?
The DM decides.
The spell description for awaken reads:
the awakened creature chooses whether to remain friendly to you, based on how you treated it while it was charmed.
No other guidance is given. Since the DM is the controller of all NPCs, which the creature is, the DM makes this decision based on how that creature would respond to how it was treated while charmed. If the DM decides to use some sort of roll for this, that is their prerogative. The few times I have had players use the spell while I was the DM, it was always abundantly clear what sort of choice the awakened creature was going to make when the time came, so I don't imagine assigning some random chance to it will make sense in most situations, unless you really are just unsure what to decide as the DM.
Based on your comments and the wording of the spell, it sounds to me like this is an XY problem. You ask about X (Awaken), because that is where the disagreement arose, but the real problem is Y (your DM is choosing to run NPCs and/or the whole campaign in a way that you disagree with). Unfortunately, it wouldn't really be practical to write a rule that essentially says "DMs have to be good at their job," so there will always be an element of subjectivity around how a DM "should" make this sort of decision. The rules intentionally hand a lot of control over to the DM, in order to empower the DM to confront you with interesting and varied campaigns and scenarios.
As for what you should do: I would advise you to talk to your DM, preferably in private. Do not focus on the rules, because the rules explicitly allow the DM to do whatever they want. Instead, focus on how the DM's style of campaign is making you feel. Use "I" statements - don't make it sound like you're assigning blame (e.g. "When you decided to call for a roll for the songbird, I felt like I was just playing a dice game, and not like I was playing a character in a story. It took me out of the fiction."). It is probably also a good idea to ask your DM what the roll was intended to represent, and why your DM chose to call for a roll. You can (if necessary) cite the rules for the proposition that it's up to the DM, but try to avoid making it sound like you're second-guessing your DM's choice. Instead, focus on the DM's reasoning. It's possible that your DM had a different interpretation of the interaction than you did.
Some DMs are more mechanically-oriented, and some are more story-oriented. Your DM may or may not be sympathetic to your concerns. There are a wide range of possible outcomes to this conversation, from your DM absolutely refusing to have the conversation in the first place, all the way to your DM retconning the entire session. The important point is that your goal is not to "win the argument." Your goal is to figure out whether you and the DM have any common ground in what a D&D campaign should look like and how it should be run. If it turns out that your DM is unwilling to accommodate you, then you have a few choices:
- Get used to playing D&D as a dice game, and not as a story game. Stop investing time and effort into roleplaying your character, and just go with the flow. If you have the time and inclination, consider joining a different campaign and roleplaying there instead.
- Discuss with other players, and see how they feel. If they agree with you, then you have a stronger case to go back to the DM. Bear in mind, even if everyone disagrees with the DM's way of doing things, the DM is not obligated to change things. They might just decide to stop running the campaign instead.
- Leave the campaign.