Only the playoff winner is guaranteed promotion.
There is also a bot cleanup, where additional teams are promoted to replace any bots. Last season, the criteria used was: Rank in conference and regular season wins. It doesn't matter how a team does in the playoffs as far as the secondary promotion. This process is repeated for each pair of divisions, so that any bots that are relegated from the 1st to 2nd division, will also be relegated to the 3rd division, etc.
If you look at last season's standings for the EBBL, you will find that 12 of the 16 teams from Season 3, are in D.III for Season 4. So these teams were bots at the end of the Season. 4 would have been relegated as part of the normal pro/rel. And then 8 more as part of the bot cleanup. The 8 additional teams, were the other 4 conference winners (all playoff winners happened to win their conference regular season), and 4 2nd place teams with the best record. It is just coincidence that there was one from each of the 4 D.II leagues.
This season, there are only 2 bots in the EBBL, and both are in 8th place and will relegate normally, along with two active teams. So only the playoff winners will promote from D.II.
There should still be some additional promotion opportunities from D.III. For example the two bots that relegate normally from the EBBL to D.II will be relegated an additional division in the bot cleanup.