gashacon

Les Bessant

WordPress 3.5 introduced a new feature – when images are inserted into posts, the title attribute is not included in the image tag. This was done with the best of intentions relating to accessibility, as documented on <a href="https://core.trac.wordpress.org/ticket/18984" rel="nofollow ugc">Trac</a>
Unfortunately, this causes problems for some Lightbox plugins, quite apart from stopping image tooltips from appearing.
This plugin hooks into the media_send_to_editor filter and inserts the image title into the html inserted into the post.
The original author, LesBessant, sadly passed away and in the meantime the original plugin was closed. I plan to keep the plugin up to date whenever an update breaks it.

IMG Title Restore

Restores the title attribute when images are inserted into posts

Vadim Bogaiskov

Media file (image) does not contain field for title attribute, only for alt attribute.
Plugin add text into title attribute from alt attribute when image is inserted into post if title attribute is empty.
As alternative see plugin <a href="https://wordpress.org/plugins/restore-image-title" rel="ugc">‘Restore Image Title’</a> by Les Bessant. 
The ‘Restore Image Title’ inserted the post title into title attribute.

Title like Alt

Restores the title attribute from Alt attribute when images are inserted into posts

IMG Title Restore vs Title like Alt