You can take a bus from SeaTac to Puyallup via Federal Way TC - Bay 5 in around 1 h 42 min.
How to get from SeaTac to Puyallup
From International Blvd & S 176th St - Bay 1 bus to Federal Way TC - Bay 5 then line 402 bus to Meridian S & 6th Ave SW. 1 h 42 min $4. From International Blvd & S 176th St - Bay 1 line 180 bus to Kent Station then train to Puyallup Station. 1 h 46 min $5. From SeaTac taxi to Puyallup. 29 min $154. From SeaTac drive to Puyallup. 29 min $2. From Seattle Airport towncar to Puyallup. 28 min $92.