I don't think that's the case at all.

First off, your explanation doesn't really work well. Let's say one group believes in A, B, and C, while another group believes in just A. Sure, all of the smaller group's demands fall under the demands of the larger group. A falls under the umbrella of the first group, but the second group doesn't believe in B or C. They have different beliefs, even if all of the smaller group's beliefs fall under the umbrella of the larger group. Maybe the second group doesn't want to be associated with B or C. What if someone formed a group that was everything that feminism believes in plus they believed in imaginary lizard people. Would feminists really be part of the "feminism + lizard people" movement, simply because all of feminism's demands fell under the larger movement's demands? Of course not.

The other issue is that your explanation completely ignores the right to free association. People have the right to identify or not identify with any group they wish. Are you a member of a group just because someone else decides you are? Or because you decide to be yourself? Your argument seems to deny agency to those who would wish that they not be labeled feminists.

Finally, there's the issue that the entire premise of feminism being for "all genders at all times" is dubious at best. One doesn't have to look far to find self-described feminists saying things which clearly aren't in the best interests of other genders. Are they not real feminists? After all, some of them clearly don't support men in any capacity. If they aren't real feminists, why don't you speak out against them? Why would you force others to be associated with feminism while doing nothing to distance yourselves from "feminists" who clearly don't care about other genders? Feminism is an incredibly fractured movement, and it seems incredibly intellectually dishonest to just assert that as a general movement it fights for all genders. It's even more intellectually dishonest to say that anyone who would disagree with that just doesn't understand, and is really a feminist. Again, that seems to totally deny the agency of others and their right to disagree.

It sounds like the intent of this is for feminists to decide for other people that their movements are really feminism, and if those people disagree then they're just mistaken about what feminism really is. That sounds like a sleezy attempt to strong-arm everyone into supporting a movement which they may not actually support. I believe in equal rights for all genders at all times, but you don't get to just decide for other people that they're part of your equality movement and then claim that any disagreement is really because they don't understand your movement.