there are a few things that appear to be making this happen.
The first is that tasks 3-6 have no predecessors. as such, they are all happy to start at the same time unless something tells them otherwise- for this, resource levelling is the key item as it will not let one task using founds (for example) start if resources are not available (as you know).
second problem is that you have actual progress plotted which doesnt look right (task 4). this telling project that you have not started task a, but work on B has been partially completed. as such, you are showing progress in the future. If this was the case then the status date would need to be after the partial completion of task b, which would mean that task A must be complete. To cure this, either set the status date to reflect the progress in task 4, or remove the % completion.
in sample A, the start date for task 3 is earlier than sample B - you need to set a constant date for the programme (in project information)or if will push task A back so it it complete before task b, unless you have a "SNET" constraint, which forces the task to split as the actual progress, or % complete, in task 4 will fix the work.