Non-local confinement bifurcations inside and around internal transport barriers (ITBs) with a ms timescale (ITB events) have previously been found in JT-60U reverse shear (RS) and high-βp plasmas. ITB events are observed as the simultaneous rise and decay of Te in two zones. They are created by an abrupt non-local reduction (or increase) of heat flux inside 30–40% of the minor radius. Under sufficient neutral beam power Pnbi (above ∼8 MW for the 1.2–1.5 MA/3.8 T pulses described below), ITB events were previously detected at various qmin values. However, the role of qmin equal to 3.5, 3, 2.5, 2 is not obvious for ITB formation. In this paper, we focus on new features of ITB evolution near low-order-rational values of qmin. The formation of a stronger ITB and its further splitting into two radially separated ITBs is described. These ITBs are located in both positive and negative shear zones of a plasma with L-mode edge. The similarity of space–time evolution of Te and Ti at sufficient power is highlighted (even when the variation is significant and complicated in space and time). Within errorbars, ITB splitting occurs as qmin passes through 2.5. The similarity of space–time evolution of Te and Ti suggests a similarity in the qualitative behaviour of electron and ion heat diffusivities in time and space. The temporal formation of an ITB in the zone with small positive shear, while qmin passes through 3 (after periodical improvements and degradations via ITB events with 8 ms period) in H-mode, with Pnbi = 8 MW, is described. At lower powers, ITB events are observed only near rational values of qmin. In weak RS shots with Pnbi = 4 MW, transport is reduced via ITB events during 0.08 s at qmin = 3.5, and repetitive short-term phases of reduced transport are observed as qmin passes through 3. The behaviour of Ti looks different. The difference in Te and Ti evolution, which was detected regularly under low power, probably indicates a decoupling of Te and Ti transport.