While hard credits should appear on a contact's record immediately after the donation is recorded, soft credits are calculated in a batch process. Therefore, don't be alarmed if you're not seeing soft credit totals on a record right away.

The soft credits are recalculated in a batch process in the Partial Soft Credit Settings tab.

Click Recalculate Contact Rollup Fields in the Partial Soft Credit Settings tab.

Then you will see soft credits accurately counted.