Much of the time all he does is toss a rose, cheer them on because the enemy, uh, lets him for some reason, and vanish. He's completely flat as Tuxedo Mask most of the time and either ends up as kinda pointless or as a sort of a deus ex machina.
I would say that Tuxedo Mask seems flat because the first 13 episodes of the anime (along with Jadeite) are pretty flat.
Deus Ex Machina is when the hero is saved by a power that hasn't been properly introduced, and the audience can't reasonably expect it to happen. The writer paints themselves into a corner and can't think of a way out, so they pull "just anything" out of their butt to move the story along. It doesn't mean that anything and everything which saves the hero is automatically bad. Tuxedo Mask was properly introduced in the first episode of the anime, and his reason for being there is completely reasonable (he's looking for the crystal, same as the villains are). People give him flak for "saving" Sailor Moon, because that's somehow anti-feminist, but Usagi's not a fighter and is constantly in need of saving (especially early on in the series), often by other girls. But then people give him flak for
not doing enough to help, since he gives Sailor Moon space to
become a fighter, when he could be one-shot-killing all of her opponents for her, even though he's not a Hero of Justice and has no stake in the fight. He's damned if he does, and damned if he doesn't.
The enemy lets him speak because a powerful opponent just stepped into the fight, fired a warning shot, and
took center stage for a few minutes.
In the first episode, Tux stopped the fight, gave Sailor Moon some words of encouragement, then Luna told Sailor Moon to use the tiara, while Tux sat back and watched her win.
In the second episode, same thing, but this time Tux left/went back into hiding before the fight resumed.
In the third episode, Sailor Moon beat the MOTD without assistance (unless you count Luna), but then Jadeite showed up and completely overpowered her. So Tux threw a rose and threatened Jadeite, forcing a very powerful opponent to back down through pure intimidation. This shows what Sailor Moon's up against, and illustrates the hill that she still has to climb.
Episodes 4-5-6, Sailor Moon takes out consecutive MOTD's with no problems (or at least, nothing Luna can't sort out).
In episode 7, Sailor Moon gets trapped in glass, so Tux fires a shot from the sidelines to shatter her prison without hurting her. The MOTD ignores Sailor Moon and tries to go after Tux, so Sailor Moon shoots her in the back.
In episode 8, Sailor Mercury appears and saves Sailor Moon.
In episode 9, Moon and Mercury confront an MOTD on her own other-dimensional turf, and Tux finds and breaks it's real-world source of power, giving them an unseen and uncredited assist.
Episode 10, Sailor Mars kills the MOTD, while Tux lurks in the background picking up survivors and securing everybody's escape route.
In episode 11, Moon and Mars challenge another MOTD on her home turf, and get caught in a trap. Tux breaks the monster's hold and then backs off, the Senshi retreat and find Mercury, and the three of them take down the MOTD.
In episode 12, there was no reasonable way for Tux to join the fight, so he didn't. Moon/Mercury/Mars gang up on the MOTD, and Jadeite is about to throw down with them when Beryl interrupts the fight to scold Jadeite.
In episode 13, Jadeite gets the fight he wants, but Tux interrupts when things start going badly. This time Jadeite's not willing to run away like he did before, so he attacks Tux and... appears to kill him? This scene is really janky, and I'll blame Toei. Jadeite claims victory and spouts some misogyny before attacking the Sailor Senshi (which is stupid because his master is a woman), and the Sailor Senshi respond to Jadeite's misogyny instead of responding to the death of their comrade. This scene is really messed up, in the direction of being "too feminist" for it's own good. Mercury throws up a cloud cover, Moon acts like bait, and Mars sticks a "kick me" note onto Jadeite's back. Jadeite is defeated but not killed, and Beryl finishes the job. Tux reveals himself as not dead, in fact, there doesn't seem to be a scratch on him. He tricked Jadeite and faked his own death so that he could watch the Sailor Senshi beat up Jadeite (after buying them a momentary distraction). It's pointed out that he also tricked the Sailor Senshi into thinking he can jump off buildings.
All of this is in line with a character who isn't part of the fight, but wants to see Sailor Moon win. He sits on the sidelines and interferes just enough to protect Sailor Moon while allowing her and her friends to fight their own battles and learn to protect themselves. Even in these rough first episodes, Sailor Moon's growth is very steady and deliberate, and Tuxedo Mask is a big part of that.