Quantum AND† gate

Question

In the paper Implementing Grover oracles for quantum key search on AES and LowMC, the authors use a different construction of AND gate and its adjoint rather than the Toffoli gate to decrease the T-depth at the expense of 1 extra qubit. I am trying to implement the adjoint circuit in Qiskit which is shown in the figure.

This is my implementation in Qiskit

q = QuantumRegister(3)
c = ClassicalRegister(1)
qand_dg = QuantumCircuit(q,c)
qand_dg.h(2)
qand_dg.measure(2,0)
if(c):
    qand_dg.x(2)
    qand_dg.s(1)
    qand_dg.s(0)
    qand_dg.cnot(0,1)
    qand_dg.sdg(1)
    qand_dg.cnot(0,1)

I converted this to instruction and tested it. For values 00, 01, 10, 11 (using NOT gates), I add a Toffoli gate and then add qand_dg instruction. Below is the code for testing.

for i in range(4):
    x = bin(i)[2:].zfill(2) # Convert number to binary with 2 bits
    qc = QuantumCircuit(3,4) 
    
    # Encode the value of x in the quantum circuit
    for index, j in enumerate(x):
        if j == '1':
            qc.x(index)
    
    qc.toffoli(0,1,2) # Apply the toffoli gate
    qc.append(qand_dg_gate, range(3),[0]) # Apply the quantum and adjoint instruction
    
    qc.measure([0,1,2],[1,2,3]) # Measure the qubits
    
    # Simulate
    counts = execute(qc, backend=simulator, shots=shots).result().get_counts(qc)
    
    res = list(counts.keys())[0][::-1] # Result
    actual = x + str(int(x[0])&int(x[1])) # expected result
    
    print(res, actual)

This gives different outputs on different runs.

1. 

2. 

Can anyone help me understand this behaviour?

I also tried implementing the circuit in a different way using the controlled operation. Circuit is shown below:

This also had the same problem. Moreover, this circuit's T-depth is 6 calculated using the below method

qc_t = transpile(qc, basis_gates=['cx','x', 'h','t','tdg','s','sdg'])
print("T-depth:",qc_t.depth(lambda gate: gate[0].name in ['t', 'tdg']))

Why T-depth is 6 having no T-gates?

I used the following code to see the transpiled circuit:

qc_t = transpile(qc, basis_gates=['cx','x', 'h','t','tdg','s','sdg'])
print("Depth:",qc_t.depth())
print("T-depth:",qc_t.depth(lambda gate: gate[0].name in ['t', 'tdg']))
print("Width:",qc_t.width())
print("Size:",qc_t.size())
print("Operations:",qc_t.count_ops())

The output is this:

Without decomposing quantum and gate:
Depth: 8
Width: 4
Size: 8
Operations: OrderedDict([('s', 2), ('cx', 2), ('h', 1), ('measure', 1), ('x', 1), ('sdg', 1)])


After decomposing quantum and gate:
Depth: 8
T-depth: 6
Width: 4
Size: 8
Operations: OrderedDict([('s', 2), ('cx', 2), ('h', 1), ('measure', 1), ('x', 1), ('sdg', 1)])

Drawing the transpiled version of the circuit, the output is the same as the original one.