PDO connection via INI parser classes
Structure

Your IniParser should be the only part of your code that is aware of how the ini file looks internally. That's the whole point of the interface: With it, you can parse different kinds of files (or even retrieve the data from something else). If the file structure changes at some point, you should only ever have to change your IniParser class, nothing else.

But right now, that isn't the case. Your Connection also needs to know how your file looks. To fix this, I would add explicit getters instead of the generic getter you have right now. So you should add getEngine, getHost, etc to your class. This has the added benefit that you can validate them (see that they exist, etc) as soon as you parse the file, instead of when you are using the credentials.

Then of course your naming doesn't make that much sense anymore. So I would rename Parser to ICredentialsParser and IniParser to IniCredentialsParser.

You might also think about passing the names of keys to it as well instead of hardcoding them inside the parser. 

If you do all this, your Connection class is decoupled from the ini file itself, and also, your IniParser gets more meaning (before, it was more or less only a wrapper for parse_ini_file).

parse and continue

If possible, I would avoid continue. In some cases it makes sense, but most of the time, it makes code harder to read. Your code could look like this:

        if (!$this-&gt;isValidated('values', $credentials, $section)) {
            throw new Exception("Values or section doesn't exist");
        } elseif ($key == $section) {
            $this-&gt;data = $values;
        }


Misc


your isValidated('values', $credentials, $section) call is inside a loop, but doesn't use the loop variables, so you should move it out of the loop.
I would create separate isValidated functions, as they don't share any common code (the way you do it just complicates things). You can name them isValidFile and hasSection.
naming: most of the time, I see open and close for the operations you are naming initialize and terminate. Your names are not bad, just unconventional. I would go with the general convention.
naming: isValidated would sound a bit better as isValid.
isValidated should probably be private.
in PHPDocs, it's always good to write why an exception is thrown.