I work a tubular cast on for 3/3 ribbing the same way I work it for 2/2 ribbing; start with a provisional cast on, then a 1/1 ribbing, then twist the stitches to get what I actually want. The knits stay knitted, the purls stay purled, and the eye is happy to see a smooth transition.
Cast on the number of stitches you want to have in your ribbing, a multiple of 6.
Row 1 (RS): Cast on a multiple of 6 using the waste yarn provisional cast on method.
Rows 2 – 3: (Sl, p) across, turn.
Row 4: (P, 1/1 RPC, p, 1/1 LPC) across, turn.
Rows 5 – 6: K2, (p3, k3) until last st, p1.
Round 1: Cast on a multiple of 6 using the waste yarn provisional cast on method.
Round 2: (K, sl wyif) around.
Round 3: (Sl, p) around.
Round 4: (K, 1/1 RPC, p, 1/1 LPC) around.
Rounds 5 – 6: K2, (p3, k3) until last 2 sts before eor marker, p2.