Contribution count does not reflect number of contributions
From the screenshot, it seems like the first contribution is done via test mode. 

FYI, test contributions are not included in the count on the tabs. Though not sure why the second one is not included. Can you add a little more information for the second row of how it is done, civi version etc ?

Update: Also make sure the financial_type_id used for the contribution is enabled from Administer -&gt; CiviContribute -&gt; Financial Types.

Path - civicrm/admin/financial/financialType?reset=1.