If the wall or the plaster is wet (for example, a newly-built house where the walls were exposed to rain before the roof went on; or if there has been a water leak) then it can take months for the walls to dry out.
In this case you can get special porous paint, with no vinyl. Dulux Trade Supermatt is the best known of these. Builders buy it in 16 litre tubs. It allows the wall to dry out without pushing the paint off, and looks quite decent. However it is nowhere near as durable as a modern vinyl emulsion, and will not stand much cleaning or rubbing. The formula trades off durability against porosity. So although it is OK on ceilings, on walls it is usually overpainted within a year or so, at some convenient time, before it gets too scuffed and shabby.
If the wall is an old dry one, then you don't need a porous paint. Leave it a week or two to dry fully pale pink and matt. Any shiny brown patches are still wet. It may help to rub it over with an old damp towel to remove any loose plaster dust from the surface. Open windows are better for drying than heat is.
When painting bare plaster (old or new) apply one or two mist coats of emulsion thinned with water. The mist coat will soak in and disappear. You will know when you have applied enough to kill the suction when the wall no longer sucks your brush dry. Once misted, you can apply your decorative paint.
For economy, you can use matt white emulsion for the mist and first coats, because it is cheaper than colours and will highlight to the eye any remaining defects that you need to correct before the finish coat. It also makes you feel you are not living in a building site, and reduces the amount of (expensive) finish paint you need.