Your understanding is correct. From $V=IR$ if voltage stays the same while resistance is increased, the current should be decreased.
But if you have heard of another equation $I = \frac{Q}{t}$
If current(I) is increased and the charge $Q$ is fixed (Charge is fixed if the power supply is from power cells like battery). Time will be decreased.
Which means that
The charges are moving faster! Because numbers of charge are fixed by the size of battery.
Imagine a four lanes road. Then in 300 meters ahead, there is a construction for road maintenance for three lanes. Making only one lane available to pass. Cars from 4 lanes must combine into one lane, making traffic jams and cause everyone to get home slower.
4 lanes road = Normal wire
Construction = Resistors
1 lane road and traffic jams = Problems cause by resistance.
Cars = Electrons
Home= + terminal of battery
Like some phone battery have 10000mAh. Which actually is the value of $Q$ but in milliamperes * hours not ampere * seconds. So 1 mAh is equal to 5/18 Coulomb.
I hope you understand my explanation.
