Q:

Is PHPmyadmin "SAAS"? 

AFAIU a SAAS software is any software which is runs on a browser and performs a certain service, (aside of giving a way to contact the owner of that software) and is also aimed for reuse, whether if it's gratis or not. 
Is PHPmyadmin, the Database Management Tool (DMA) SAAS actually? 

A:

phpMyAdminitself is not "Software as a service".  It could be part of such a service, but this would be an unusual case. 
"Software as a service" means a customer pays a service provider for the use of a software package, with the provider being fully responsible for maintaining, administrating, and hosting the software. 
phpMyAdmin itself is open source and hosting it as well as the underlying database, ist completely up to the users.  
Even a case where a company hosts a database and allows customers to access this DB via phpMyAdmin would not typically be called "Software as a service", because SQL databases are nowadays seen as infrastructure rather than software that is directly used, and administrating a database (which is what phpMyAdmin  is for) is exactly the kind of thing that the customer isn't supposed to be bothered with in a SaaS model.