Kind of sounds like you are wanting to recreate a Jobo processor. They pump the chemicals into the tank in about 10 seconds, and they allow a 15 sec drain at the end of each process. A stop bath is only 30 seconds, so the chemical needs to get into the tank fairly quickly. Similarly, if you have a 5 or 6 min developing time, it can't take a minute to get the developer into the tank - that's a big portion of the developing time. It would also depend on how the film is configured, if it take a min to get developer in, is part of the film in contact while the developer is filling? If so, then you are going to have some part of the film in contact with developer for a min longer than other parts, and you'll have uneven development.
The rinses are connected to the mains water, but after developer is a stop bath, which is treated as it's own chemical. That's fully programmable with a Jobo, so it could be a water rinse in place of stop.
The Jobo uses air to move the chemicals, it has a selector to direct air to the correct chemical storage bottle, which then pressurizes the chemical storage bottle slightly. There is another tube that then goes to the tank with the film in it, and the air pressure pushes the chemical out the delivery tube into the film tank. I don't know how it meters the amount of chemical it pushes through, but it does somehow.