You are initializing a carousel inside of a tab which is not visible in the browser when the browser loads content. This makes the Javascript for the carousel to not initialize the carousel properly since the content is not active at the time of window load. The reason resize works – the Javascript kicks in to reinitialize the carousel based on changed attributes.
To summarize – you cannot use carousel inside tabs or accordions which can hide the content and hence hampering proper initialization. Pls move the same out of the tab and you should do fine.