Sorry you for the late answer.
I see that you can solved the problem, thank you for your feedback.
Yes, sometimes some CSS adjustments needed for the right look and feel, because every theme is different, and they are modify the appearance of Google CSE search field and button differently.
Using CSS you can achieve other appearance, so you can make more adjustments. However Google CSE has a rather complex html structure for displaying search field and search button, so sometimes it is hard to find the most appropriate CSS settings, but it ensures a wide range of displaying possibilities.