Have you experienced a 'dualogic' type car before? What you are feeling could be characteristic.
The dualogic is not an automatic gearbox as we've known for years, but is a manual gearbox and clutch, operated by hydraulic servos, controlled by a computer.
When you select D, a servo depresses the clutch, and another selects 1st gear. When you release the brake, and then push the accelerator, the clutch servo gently releases to engage the clutch, and away you go. If the clutch is replaced there's a learning process, otherwise it adjusts as it goes.
Once on the move, as each next gear is needed, a signal is sent to the engine computer to release the accelerator, which should coincide with the clutch being released, the next gear being engaged, then the clutch is re-engaged, supposedly simultaneously with the power being re-applied. What we do when operating a manual gearbox.
The main characteristic of this type, is the release of power during the gearchange, which can take a little getting used to, if previously having had a 'normal' autobox. Eventually you'll get used to it.
It is worth ensuring the servo oil level is correct. There's a small reservoir on the side of the gearbox, difficult to access, and uses different oil to the main gearbox. Also worth ensuring that the left brake light is working, with good clean connections. The gearbox control seems very sensitive to this lamp, and failures here have caused strange issues. With a helper holding the brake on, stand 50m away, and see if both lamps are equal brightness.
Ensure when driving, the left foot does not rest on the brake pedal. If the brake switch operates, the gearbox will get upset, as it does not like go and stop signals together.