@AfonsoSalgadoSousa there are two questions here: 1) why time is not printed and 2) how to print intermediate metric value.
Q1: during the evaluation we typically run a single epoch and evaluator.state.times does not contain per-iteration times, but only epoch and total run. It would be better to use ignite.handler.Timer for iterations.
Q2: to print intermediate metric value we have to compute it per-iteration <=> call metric.compute or metric.completed, see the example below.
Here is an example of how to achieve what you would like :
import time
import torch
from ignite.engine import Engine, Events
from ignite.metrics import Accuracy
from ignite.handlers import Timer

def eval_step(engine, batch):
    return batch


evaluator = Engine(eval_step)

acc = Accuracy()
acc.attach(evaluator, "accuracy")

timer = Timer()

# Compute intermediate metrics
@evaluator.on(Events.ITERATION_COMPLETED)
def compute_and_measure():
    acc.completed(evaluator, "accuracy")
    # added sleep to emulate an amount of time taken by processing a single iteration
    time.sleep(0.1)


@evaluator.on(Events.ITERATION_COMPLETED(every=1) | Events.COMPLETED)
def log_info():
    metrics_output = "\n".join(
        [f"\t{k}: {v}" for k, v in evaluator.state.metrics.items()]
    )
    print(
        f"\nEvaluation time (seconds): {timer.value():.8f}\nValidation metrics:\n {metrics_output}"
    )


bs = 32
n_classes = 10
    
data = [
    [torch.rand(bs, n_classes), torch.randint(0, n_classes, size=[bs, ])]
    for _ in range(8)
]
    
    
state = evaluator.run(data)
print(state.times)

Output:

Evaluation time (seconds): 0.10191662
Validation metrics:
 	accuracy: 0.03125

Evaluation time (seconds): 0.20312049
Validation metrics:
 	accuracy: 0.0625

Evaluation time (seconds): 0.30411697
Validation metrics:
 	accuracy: 0.125

Evaluation time (seconds): 0.40528948
Validation metrics:
 	accuracy: 0.125

Evaluation time (seconds): 0.50620632
Validation metrics:
 	accuracy: 0.125

Evaluation time (seconds): 0.60733969
Validation metrics:
 	accuracy: 0.125

Evaluation time (seconds): 0.70837395
Validation metrics:
 	accuracy: 0.12053571428571429

Evaluation time (seconds): 0.80952449
Validation metrics:
 	accuracy: 0.109375

Evaluation time (seconds): 0.81010838
Validation metrics:
 	accuracy: 0.109375

{'EPOCH_COMPLETED': 0.8085811138153076, 'COMPLETED': 0.8087835311889648}

HTH