It's not really an issue in Gen 1 and 2, because due to badge boosts and how EVs (or whatever were called back then) worked, the more you progress through the game, the less the level difference matters. You're still more powerful than your opponents even if you're underlevelled.
On top of that, add that most Johto important trainers have pretty terrible teams, and the AI is mostly crap, and it's not really a surprise that by the time you reach Red you can defeat him even if your team is 20-30 levels below him.
The remakes made it somewhat more challenging, but not a lot either. Honestly, you don't even need six Pokémon to beat Johto, actually you don't really need six Pokémon to beat any of the main line games because the only serious trainer with six Pokémon that you'll ever face (before the post-game) is the Champion. You can do totally fine with five, or even four depending on the game.
But if you want a full team, and don't want to be ever underlevelled, well, I don't recall it being much of an issue keeping up with the level curve, you'd probably want to avoid Pokémon with slow growth rate, pace your team additions (try to get your last Pokémon not too early but not too late in the adventure either), explore and do the side-stuff (Alpha Ruins, Union Cave, etc.) once you get new HMs, and maybe save Rare Candies for your final addition. It's not a big deal.