Got Xbox Game Pass Ultimate on both console and pc but didn't got Spotify Premium

Normally you should get the code via message on your xbox within around 10 business days. If you waited that time i would recommend to contact the support team like {Parity} mentioned.

Before going straight to suppprt, double check the terms of the offer:

*Limited time offer valid, only in USA and UK, while supplies last. May take up to 10-business days for new members to receive Spotify Premium code via Xbox Message Center. Not valid for existing or previous Xbox Game Pass Ultimate or PC (beta) members,
other exclusions apply. Limit 1 offer per account. Codes will be delivered through email before 3/20/2020. Offer cannot be combined with any other offer. After promotional period, subscription continues to be charged at the then-current regular price (subject
to change), unless cancelled. Plus applicable taxes. Credit card required. Game catalog varies over time. Spotify disclaimer: $9.99/month after trial. Codes available while supplies last. Open only to users who haven't already tried Premium. Offer ends 4/1/2020,
codes must be redeemed by 10/1/2020. Terms and conditions apply. Please visit https://www.spotify.com/us/legal/Spotify-6m-Xbox-offer for more details.

I did get the code for Xbox Game Pass Ultimate (did came with Spotify Premium as well), and redeemed it but didn't get me Spotify Premium, but I'll see what I can do

You didn't get code or not at all?

Reach out to
Xbox Support for assistance with that.

The best way to reach Live Support would be here:
Xbox Support

Step 1 ----Select Xbox One

Step 2 ----Select See other options

Step 3 ----Select topic (Ex. System Update)

Step 4 ----Select "Show contact options"

Step 5 ----Select request a call from support