Assuming the amp provides enough power to adequately drive the speakers to your preferred listening level, the two most important factor in how the music sounds are source firmware and the speakers.
Since your speakers sound decent on most stuff, I'd suspect the recordings but, looking at that leaflet you provided, those speakers, with a sensitivy rating of 85 decibles, are incredibly inefficient*, which means they need quite a bit of power to play loud and clean. With that amp on;y being speced for 15 watts at 10% distortion (or 9 clean watts), that could definitely be a problem as well.
Specifications: • Power output: 15W x 2 (4 ohms, 10% THD), 9W x 2 (4 ohms, 0.03% THD), 10W x 2 (8 ohms, 10% THD), 6W x 2 (8 ohms, 0.1% THD) • Headphone power output: 60mW x 2 (16 ohms, 1% THD), 120mW x 2 (1% THD), 100mW x 2 (32 ohms, 0.01% THD) • DAC THD+N: 0.008% @ 1 kHz • Signal-to-noise ratio: 98 dB • Dynamic range: 98 dB • Dimensions: 4.17" W x 1.65" H x 7.1" D.
Either find incredibly efficient speakers (98+ decibles sensitivity/efficiency rating) or get a more powerful amp. I'd recommend the latter.
* Most decent small speakers are.