Grad programs usually require that universities send transcripts directly to them. However, some online application systems list what materials they have received so far, so it makes keeping track of your transcripts easier. If it's close to the deadline (or past it), grad programs often call you to ask for missing materials.
Remember that if you're not sending something directly (GRE scores, transcripts, recommendation letters), they'll understand it's out of your control, so they'll be a little more lenient on the deadlines.