if it is your first then you are prob fine. YOu have 3 official bans before your perm ban. The way it works is after your automated 24 hour ban by the tribunal Riot then takes over and decides what ban to give or to overturn the tribunal decision. Their decision can take up to a week after the tribunal decides on non perm ban judgements. In that time while you have been found guilty by the tribunal you continue to play and can rack up reports easily if you are truly toxic. When riot makes a decision it is possible to have enough to be back in the tribunal again and be banned not long after your previous ban. All games prior to the decision of the tribunal that you were reported in are removed; however, the "grace period" between judgement by Riot is fair game.
EDIT: While I may be off on the estimates, the information provided is what I've been able to gleen from things Riot has said and the information given by players who have been banned then rebanned within days of their previous ban ending and my own experience in judging cases. So while speculation, it is a plausible explanation.