What version of eM Client are you using? Check if you have the latest version from the Release History.Upgrade if necessary and see if there is any difference.
If you have a Pro License, you should open a support ticket directly with eM Client.
Turns out when you compose a message using the context menu it auto switches format to plain text. Switching it back to HTML renders the signature properly but you have to do it manually regardless of the settings.
Setting mail format for reply to HTML solves this issue.
eM Client autodetects message format as plain text by default when attaching a file using the context menu.
I am using an 8.1 internal build and it works fine with the default setting as in my screenshot. Wonder why the reply format has anything to do with it? Maybe this is something that has now been fixed and will be in the next release.
It might be due to OS language as the default message that appears when composing mail using the context menu is localized. I have eM Client language set to English but my OS is in Polish.