Don't forget to wash your hands after you have played outside.
Make sure you remember to wash your hands after playing outside.
chanmitsuさんのおっしゃるように after you have played を使うので下のように言えますね。
Don't forget to wash your hands after you have played outside.
「外で遊んだあとは手を洗うのを忘れないで。」
after playing outside とも言えます。
Make sure you remember to wash your hands after playing outside.
「外で遊んだ後は、必ず手を洗うのを忘れないようにしてね。」
after playing outside の代わりに when you come inside(外から帰ったら)を使って言っても良いです。
ご参考まで!