When multiple things happen at the same time, you get to choose the order they occur in. Therefore, you could deploy the Vine Tree (using a Seedling Pod for example) and then choose to place your vine markers. In which case, you could definitely place an extra Vine Marker using the Vine Tree's ability. However, since you are already outside of the Planning Phase, the Vine tree will not have any spells that it can cast through the Vines during the same deployment in which it itself was cast.