Regardless if you are shipping with your account, on behalf or billing a third party, the tracking numbers should be updated in the WMS either when processing the order (as long as the WMS supports it), or after you manifest (supported by all WMS integrations).
If you see the tracking information in techShip but not in your WMS after manifesting, this could relate to several issues, ranging from system issues to human error.
To make sure everything has been done properly prior to reaching support, verify that:
1) You processed and not voided the orders
2) The orders have been packaged in the WMS (3PL Central only)*
3) The orders have not been closed before manifesting in the WMS (all WMSs), since techShip cannot update any information to closed orders
4) Manifested (Closed) the orders as described in this article: 02 - How to manifest [Step-by-Step guide]
5) Re-ran WMS Update in case there was a connectivity issue in the Manifest History view:
6) Generated a Shipment Detail report (as described here: How to generate and read Shipment Detail reports [Step-by-Step guide]), and confirm that the WMS Update Status column (typically column AM) shows Completed instead of Pending
If all these checks and actions were done on your end and the issue still persists, please reach techShip support.
* For 3PL Central, the tracking number is not returned at the package level when orders are not packed. To get tracking numbers on the package level you should pack orders, so the package count in 3PL Central matches what you actually ship, and instead of using the Carton Import mode 'Merge' option in Techship, you need to use 'Default' option (13 - Setting Carton Import Mode - Default or Merge mode? - [Step-by-Step Guide])
To pack orders in 3PL Central you can, for example
1) Highlight/Select a group of orders
2) Click Recalculate packages
3) Click Consolidate