Spinneraki's first time most likely occurs after the foundation of the PLF to me. Although I really enjoy thinking about them together before that and with Tomura's blue hair, but I think the likeliest chance for them to get really intimate is during that intermission of waiting for Tomura to heal before his upgrade. In my hero ultra impact Spinner has a habit of following after Tomura, asking if he's okay and being the one most concerned with his health, and being in his company the most. His life's focus has changed from Stain to Tomura, so he's seeking him out both consciously and unconsciously. Spinner is super concerned with his health and he's willing to go out of his way to obtain resources for him if he just asks (there's this one instance in mhui where Twice's Spinner double is willing to die for tomura, but thats not that important here).
Spinner probably wants to keep track of Tomura's health, since the latter doesn't take care of himself properly (e.g. his room, his sleep, doing reckless things while hurt) and with Spinner's shut-in history I think he's dedicated to not wanting Tomura to be anything like he was. This, in addition with Tomura's recent disability (lost half his hand), I think Spinner would be in charge of changing Tomura's bandages and care to his wounds. Tomura had trouble walking even with a cane at the start, so his mobility is severely limited, and no one's more willing to he a shoulder to lean on than Spinner. Additionally, Tomura has a habit of asking Spinner for things, like getting food, so it feel natural for Tomura to request Spinner (he's also most comfortable to lean on because they're the same height).
Spinner's no doctor or nurse, but he probably has some experience tending to wounds (given how abused he was in his hometown) and he wraps bandages pretty well for his cosplay. He can definitely get around to applying ointment and other treatment for Tomura as well by just asking one of the Liberation's nurses/doctors after the intial wrap up. He'd take it upon himself to tend to his wounds for multiple reasons...
1. The league are very closed off in the PLF, they don't interact with many and only do for buisiness and order, and keep to themselves during recreational time.
2. They don't trust the PLF completely, even when hawks has a good rep there, he's not allowed to see Tomura. There's also people in the liberation who are against the league, and Tomura keeps everyone who's not the league away. It would make sense if Spinner wouldn't trust someone to clean Tomura's wounds or enter his room in case of bugging.
3. Honestly I find it hard to believe any doctor or nurse to be willing to clean Tomura's wounds with how deadly he is. He stopped their whole army by just a look on his face. In MHA we don't see many healing/doctor heroes and they're usually not skilled at combat, so I don't find it too likely the PLF would have doctors skilled in combat enough that theyre not trembling in their boots in Tomura's presence, which is dangerous if you're tending to someones wounds. Tomura was absolutely unconscious during the initial operation, so thats how he got fixed up. Not sure if they'd be okay with fixing him up while he's concious.
So instead of having some random trembling nurse/maid/doctor fearing for their life while treating Tomura, his most devoted follower and closest friend Spinner, is just the better option. All he needs is instructions and equipment and they don't have to risk assailants or infiltration either.
Plus Spinner probably visits his room to play games and chat all the time since Tomura needs to focus on resting and healing. He might stay over at the start since Tomura's too injured to leave alone, he needs promptly antibiotics, ointment, painkillers etc. And eventually it might become routine. Spinner is probably his happiest during these alone moments with Tomura too, tending to his hero's wounds and playing games with his best friend. Spinner's probably so so gentle and sweet during treatment too, making sure everythings perfect and pausing to analysis Tomura's body language and expression for pain. but if anyone says anything, even tomura, he'll get defensive and snappy. Tomura's probably feeling the same sort of happiness too, getting to be pampered like a hero and afterwards gaming and laughing like his entire being is something more than bringing destruction.
ALSO! Tomura somehow knows Spinner wants to see that crumbling horizon even though they never have a conversation about it. So I get to decide when Spinner spills his guts to Tomura about how he'll follow him to the end and how devoted he is. And I get to decide how it happens too, so cue their first time. Anyone else notice how comfortable Spinner is with touching Tomura after his transformation despite when after the PLF is founded and Tomura falls to the ground he just looks over.. Almost like something happened in between these times where touching each other became comfortable.. (Delusional talk, I know Tomura was severely hurt and it was life or death during the Jaku fight).
If you've read all this, I really appreciate that you did. Thank you for indulging in my loser spinneraki takes.