Just fought a couple of siege battles as Danes with Lithuanian allies against the Teutonic orders finest castles.

In one battle I unclicked the wee box and the other I forgot so I can compare what the allied army did in similar occasions.

Well actually they behaved in a very similar way.

In both battles I was besieging when the Lithuanians arrived. Not wanting to be their cannon fodder I initiated the attack. Both times I used ladders to open up the gates opposite to where I had set up (ie in the Lithuanian half of the battlefield.) And both times once the gates were open the Lithuanians poured in and a jolly time was had by all butchering the Teutonic defenders.

Indeed on one occasion the Lithuanians actually picked one set of ladders so they could scale the inner walls of the fortress, but dropped them when they saw the gates had been rushed by my cavalry.

So controlling the reinforcements or not:

Danes + Lithuanians = dead Teutonics.