Hi Karel,
With the new driver - that is, the default driver for V14 unless you specifically chose to use 'legacy' driver, constraints are no longer placed on tasks by the scheduler codes. This was a change documented in the Change Impact guide for v14.
This means that if you want a task to start on a date different from project's start date, and the dependency of the task is not enough to pin it to a date you want, you would need to manually add a constraint on it.
While constraints are not automatically created by PPM when sending tasks over to MSP, they are created by Microsoft Project when a task is create in MSP with a later start date. So if all your tasks were created in MSP, you should expect to see constraints on them. Another important setting that will help keep things in place is an option called 'Tasks will always honor their constraint dates', judging by the picture where your tasks are showing as 'manually scheduled', you may not have the required settings put in per the Green Book.
Before setting the default make sure all projects (including the Project 1 project) are closed in MSP, so that your settings are applied to all projects.
The Green Book: CA Clarity PPM: Integration Best Practices for Microsoft Office Project
Other goodies for you (definitely check out the Scheduling Best Practice!) : CA Green Books - Project and Portfolio Management - CA Technologies
Btw the same requirements are also documented in the live DocOps page for MSP
Connie