How to show posts with multiple tags on tag.php?

get_query_var( 'tag' ) will return you 'tag1+tag2+tag3' string.

get_query_var( 'tag_slug__and' ) will return you the array of tags.

So, there are two ways to achieve the goal:

$args = array( 
    'tag' => get_query_var( 'tag' ), // string
);

or

$args = array( 
    'tag__and' => get_query_var( 'tag_slug__and' ), // array
);

It remains to be seen how do you plan to create tag1+tag2+tag3 slug.