When building prototyping boards using a stencil and reflow oven I'm still having a lot of bridges when I use fine pitch components (say 0.5mm pitch). One of the things I've realised I need to do is to make the openings in the stencil smaller for these footprints.
Simply ask the stencil shop to close up the required pad openings by a chosen percentage.
Normally in Altium they are the same size as the pads.
Yes & no. Altium gives you the ability to change the paste mask & often the default is to make the openings a bit smaller than the pad dimensions. This prevents any pooling of solder paste around the edges of the pad.
Altium treats the paste layers as layers, just like your top & bottom copper layers. Just turn on the top solder paste layer (press "L" on your keyboard) & take a look.
If you wish to change the paste expansion (or contraction), right click on the pad (you may have to unlock it first) & adjust the paste expansion to what you desire. You can select multiple pads & make a "global edit" of all the pads that are selected. Do not do an update from the library after you make these changes, otherwise the footprints will be changed back to the default library footprints.
I understand that most production houses prefer it that way as they post process the paste mask themselves.
It may be that some production shops do this, but in my experience they simply reproduce what's on the Gerber that you supply them.