Batsman Roy made an "audible obscenity" in the 14th over of Pakistan's innings after a misfield by England.
Archer, who took 0-79, showed "obvious dissent" to the umpire after delivering a wide in the 27th over.
Pakistan captain Sarfaraz Ahmed was fined 20% for a slow over rate.
His team-mates were each fined 10% for the breach as "Pakistan was ruled to be one over short of its target after time allowances were taken into consideration", the ICC said.
Both Roy and Archer have received one demerit point each, which can lead to a ban if a player gets four within 24 months.