the bottom image seems just fine, while the first image is very hard to understand. i dont know what is going on in it.
to give you some information, yes, you do have a Center. if you select the model, there will be an orange dot somewhere, THAT is the center of witch the mirror modifier will apply.
Also, click N and check your Scale, and Rotation properties on the model in object mode. They should be 1.1.1 on scale, and 0.0.0 on Rotation.
To fix this, CTRL+A and select Scale, and Rotation.
Do some research on what the different settings in the mirror modifier does, cause otherwise you will run into trouble.
if you need further help, please submit your Blend file for review, and we will take a look at it.
Also, if you need, let me know and i will make a video response explaining the mirror modifier and its settings.
If you do wish a video response, feel free to make a list of questions.