He's a bit misinformed, though. The mistaken belief that it takes 3 months to earn rewards again or to go down in punishment tiers came from Riot Lyte stating that it takes 3 months on average for players to drop one tier of punishment, but it doesn't include anything more than that.
Hextech Loot eligibility is earned back by playing games and showing you've improved your behavior;
The system will permit you to earn hextech loot once it believes you have reformed - this differs per person, and can be as quick as within a week, or as long as months, depending on your behaviour in games after your restriction.
Basically, there is no set time limit, it depends on the severity of your punishment and you showing that you've reformed.
http://boards.na.leagueoflegends.com/en/c/player-behavior-moderation/57wOcrmh-if-you-are-ineligible-for-hextech-loot-read-here-for-info-on-becoming-eligible-again
Edit: Oh ya, and you didn't lose your end of season Ranked rewards for this. The only way to lose them is to A) Have an active restriction when the season ends and rewards are distributed, B) Have an account ban (behavioral) within 3 months of the season ending, or C) Get an MMR Boosting ban at any time during the season or afterwards.